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Which of the following accurately describes the effect of increasing the sample size?​Group of answer choices​Increases the standard error and has no effect on the risk of a Type I error​Increases the risk of a Type I error and has no effect on the standard error​Decreases the risk of a Type I error and has no effect on the standard error​Decreases the standard error and has no effect on the risk of a Type I erro

Question

Which of the following accurately describes the effect of increasing the sample size?​Group of answer choices​Increases the standard error and has no effect on the risk of a Type I error​Increases the risk of a Type I error and has no effect on the standard error​Decreases the risk of a Type I error and has no effect on the standard error​Decreases the standard error and has no effect on the risk of a Type I erro

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Solution

Increasing the sample size decreases the standard error and has no effect on the risk of a Type I error.

Here's why:

  1. Standard Error: The standard error of a statistic is a measure of the dispersion of the sampling distribution. It decreases as the sample size increases because as you collect more data, your estimate of the population parameter becomes more precise.

  2. Type I Error: This is the error of rejecting a null hypothesis when it is actually true. The risk of a Type I error (also known as the significance level or alpha) is set by the researcher, not by the sample size or the data. Therefore, increasing the sample size does not affect the risk of a Type I error.

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